S = {(x, y, z) E R : 2 = x² + y°, 0 s 4}. Evaluate e* dS. ds.

Q: Use an appropriate form of the chain rule to find dz/de 1. z = 3x?y; a =t and y = t? 2. z = 3 cos a…

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Q: Let I = L,x? cos(x + 1) dx. The approximation of I using the two-point Gaussian quadrature %3D…

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Q: w = x Tan (yz), x = u2, y = e2v , z = v cos u. Find wu and wv 10.

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Q: So lve the di fferential equation dy + y - ecos x = 0,0 s x s0.5, y (0) = 0 by (a) Milne's me thod…

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Q: Given: y = f(u) and u = g(x), find dy/dx: %3D a) у %3D сos u, и%3D—х/3 -x/3 u = b) y = tan u, и 3D…

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (d) z = sin (4x + 5y); x = s + t, y = s - t

A: Given that, z=sin4x+5y ; x=s+t ; y=s-t Then we get, z=sin4s+t+5s-t⇒z=sin4s+4t+5s-5t⇒z=sin9s-t

Q: az and dz Use the chain rule to find as at sin(0) r = st, 0 = s9 + t° %3D as az at

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Q: Given dy dy dz² +2 + 5y = e dr and y(0) = 0 and = 0 find the value of y(0.1) and y'(0.1) using the…

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Q: Use the Chain Rule to find dw/dt. + y2 + z2 x = 5 sin(t), y = 7 cos(t), z = 6 tan(t) W = In

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Q: Find a. Əw dx a. aw əx and b. y (2π,1,-π) Əw at the point (x,y,z) = (2π, 1₁ - π) if w = x² + y² + z²…

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Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: Given z = 17 In(t) and y = 289 t then fir dy d'y dx?

A: Differentiate given function

Q: Given z = 14 In(t) and y= 196 t then find dy %3D dx dy ||

A: Given a parametric equation:                                    x = f(t) , y = g(t)  the first…

Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: . Evaluate ſſ,G(r)dA where G(r, y, 2) = arctan(y/x) and S is given by z = x² + y², with z< 9, r 2 0,…

A: According to the given information, it is required to evaluate the integral.

Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: If y(u) = Cos v -dv then y'(u) =

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Q: Find the solution u(x, y) of u+sin(r) uy = y for z, y ER, u(x = 0, y) = 0.

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Q: Let y, = sin(t) be a solution to t y" -y' +4 t y=0. If y(t) is the solution to the I.V.P ty" -y' +4…

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Q: Use the Chain Rule to find dz/ds and dz/dt. Z = tan(u/v), u = 3s + 6t, v = 6s - 3t dz ds dz at Need…

A: Given z=tanuv , u=3s+6t , v=6s-3t

Q: Ut for 0 <x <l u(x,0) = x u(0, t) = (1, t) = 0

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Q: Use the Chain Rule to find əz/əs and dz/Ət. (a) z = x?y°, x = s cos t, y = s sin t (b) z = 4e" In y,…

A: (a). In this question given that - Z= x2 y3 ,  x = scos(t) , y = ssin(t) And find derivative of this…

Q: |0 (x, y, z) | dV dz dr de |0 (z, r, 0)

A: In cylindrical coordinates

Q: 1.Evaluate S. (x² + y² + x²)-²ds where C is the helix x = cost, y = sint, z = 1 for 0 < t ST

A: The length dS is: ds=dtdxdt2+dydt2+dzdt2=dt-sint2+cost2+02=dt

Q: Find ow/@s and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x S+ t, y =…

A: Given that function w=sin2x+3yx=s+t , y=s-tvalue s=0 ,t=π2To find :∂w∂s,∂w∂tSolution…

Q: Use appropriate forms of the chain rule to find dz/ðu and dz/dv. Z = cos x sin y; x =u – v, y = u² +…

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Q: Given z = 15 In(t) and y =225 t then find dy da dy da?

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Q: Use the Chain Rule to find dw/dt. w = In(V? + ° + z2 x = 3 sin(t), y = 2 cos(t), z = 5 tan(t) dw dt

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Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: dz Given z = e* sin y,x u? + v2,y = uv, find - dv %3D %3D

A: Here I am attaching image so that you understand each and every step.

Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…

Q: i x Jl plaly da :J,I Ji ull rcos(@), y=rsin(@) التكامل e-(5x2+2y) dxdy

A: We have to use integration using changing the rectangular axis.

Q: Utt || for 0 < x < T u(x, 0) = x? u:(x, 0) = }cos(8x) Uz(0, t) = u„(r, t) = 0

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Q: Given z=3 In(t) and y=9t² then find dy de dy da %3D

A: We use parametric differentiation

Q: dy 3. da + y = 2xy?e"

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Q: • T/4 cos(0) f |/| f(x, y, z) dV = 9p sin(ø) cos(4) dp d0 dø, find f(x, y, z). E f(x, y, z) =|| ?

A: We have to given ∫∫∫Efx,y,zdV=∫0π2∫0π4∫0cosθ9ρ2sinϕcosϕdρ dθ dϕ Now the function which is to be…

Q: dz Use chain rule to find at (s, t) = (0, 1) if ds z = 6x + y² tan e – st, y = s² – ť. x = ebs

A: Consider a function of multivariable where and . Then according to the chain rule for…

Q: Sv? – 1),/y dy

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: T(z, Y, 2) = 1500e 2y

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Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

A: Let's find.

Q: fi at nd laplace: {e}

A: Use the formula for the Laplace Transform for the given function.

Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: dz Given z = e* sin y,x = u² + v²,y = uv, find dv

A: Using chain rule of derivative,

Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

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Q: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

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Q: Given z = 10 In(t) and y = 100 t² then find %3D dy da d'y da2

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